Ménage Numbers and Ménage Permutations
Yiting Li
Department of Mathematics
Brandeis University
415 South Street
Waltham, MA 02453
USA
Abstract:
In this paper, we study the combinatorial structures of straight and
ordinary ménage permutations. Based on these structures, we prove four
formulas. The first two formulas define a relationship between the
ménage numbers and the Catalan numbers. The other two formulas count the
ménage permutations by number of cycles.
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(Concerned with sequences
A000108
A000179 and
A000271.)
Received
January 16 2015; revised versions received February 21 2015; June 11 2015; June
15 2015.
Published in Journal of Integer Sequences, June 16 2015.
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